Calculate the Risk (Standard Deviation)of the Following Two-Security Portfolio If

question 33

Multiple Choice

Calculate the risk (standard deviation) of the following two-security portfolio if the correlation coefficient between the two securities is equal to 0.5.
$\begin{array}{cc}&\text { Variance } & \text { Weight (in the portfolio) } \\\hline \text { Security A } &10 & 0.3 \\ \text { Security B } &20 & 0.7\end{array}$

• A)17.0 percent
• B)5.4 percent
• C)2.0 percent
• D)3.7 percent
• \(\begin{aligned}
• \sigma_{\mathrm{p}} & =\left[\mathrm{wl}^{2} \sigma_{1}^{2}+\mathrm{w}_{2}^{2} \sigma_{2}^{2}+2\left(\mathrm{w}_{1}\right)\left(\mathrm{w}_{2}\right)\left(\rho_{1,2}\right) \sigma_{1} \sigma_{2}\right]^{1 / 2} \\
• & =\left[(0.3)^{2}(10)+(0.7)^{2}(20)+\right. \\
• & \left.=2(0.3)(0.7)(0.5)(10)^{1 / 2}(20)^{1 / 2}\right]^{1 / 2}=3.7 \%
• \end{aligned}\)

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